Teacher s Guide to Computers in the Elementary School

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Teacher’s Guide to Computers in the

Elementary School

David Moursund

Dept. of Computer & Information Science University of Oregon

Eugene, Oregon 97403

Preface to the 2005 Reprint

The first and second books book published by the International Council for Computers in Education were:

Moursund, David (1980) School Administrator’s Introduction to Instructional Use of Computers. Eugene, OR: ICCE. Access at http://darkwing.uoregon.edu/~moursund/dave/SchoolAdministrator.html.

Moursund, David (1980). Teacher’s Guide to Computers in the Elementary School. OR: ICCE.

The two books overlap considerable in content. Both were 48 page “booklets” and both sold for $2.50 for a single copy. Both were based on a question and answer format, and both were illustrated by Percy Franklin. The intent in both cases was to keep the books rather easy to read and non-threatening to the reader. Both sold rather well, as there was little competition at that time.

These two books were written nearly 25 years ago. I find it very interesting to reflect on the changes that have occurred in Information and Communication Technology (ICT) in education during this time period. As I was reading this 1980 booklet for elementary school teachers, I found that I was disappointed in the progress we have made.

It is easy to point the “blame” finger at all kinds of people and organizations. But, here I want to take a different approach. This particular booklet has a strong emphasis on roles of both

calculators and computers in problem solving. By 1980 (and earlier) it was quite clear to me that the focus of computers in education needed to be a focus on roles of calculators and computers as an aid to representing and solving problems. By 1980, the National Council of Teachers of Mathematics had come out strongly in support of use of calculators.

The human race has survived and prospered because of the very capable brains that people have. Among other things, humans are good at accumulating knowledge and skills, and in sharing knowledge and skills with each other. This sharing often occurs in face-to-face settings. But, this sharing also occurs through the tools that are developed and made available to others, and through written language. The past 250 years have bought us the Industrial Age and the Information Age. The tools, including the ICT tools, have significantly changed our world and the lives of people living in this world.

Reading and writing, along with the Industrial Age and Information Age “progress” have led to an exponential rate of growth in worldwide-accumulated data, information, and knowledge. From a problem-solving point of view, this means that there are a steadily increasing number of problems and problem areas that we (collectively) know a great deal about. The “we” here is people and their collected data, information, knowledge, tools, and so on. The exponential rate of growth means a doubling in some modest number of years, sometime currently estimated at perhaps five to ten years. And, the growth is accompanied by a steadily increasing number of problems that people are studying and dealing with.

Now we are getting to the crux of the matter. The nature and extent of the problems that an ordinary person is faced by in everyday life is growing in breadth, depth, and complexity. This is meant to be a strong assertion, so let’s think about it a little. The general area of health provides an excellent example. You, personally, know many things about food, vitamins and minerals, medicine, exercise, blood pressure, cholesterol, vaccinations, viruses, bacteria, infections, and so

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on than the leading physicians of a couple of hundred years ago. You have accumulated

considerable health-related knowledge that is personally important to you. And, you continue to learn more through a wide variety of resources such as your friends, the media, your doctor(s), and so on.

In recent years, the medicine and health information resources on the Web have become one of the most widely used components of the Web. There is a good chance that you have learned to use the Web as an aid to dealing with health-related problems that interest you. In the process of continuing to expand your knowledge of health-related data, information, and knowledge, you have learned that there is far more to know than you will ever know. You read and hear ads and reports from the media. You have learned that doctors and other sources of information are fallible. You have learned about recalls of various drugs that are damaging some people. Perhaps, at times, you feel overwhelmed by your need to deal with health problems.

Now add to that all of the disciplines that you have studied in school or encountered in other ways. My personal conclusion is that there is no way that I can begin to keep up—to learn about and to effectively deal with the data, information, and knowledge from all of these disciplines that is particularly relevant to my life. I believe that this situation describes all people living in our Industrial/Information Age society.

By now you may be asking, what does all of this have to do with calculators, computers, and other aspects of ICT? There are two parts to my answer:

1. ICT is contributing a great deal to representing problems, working to solve these problems, and storing and sharing the results of this work. Thus, people doing this type of research and knowledge-building tasks work need a significant level of ICT

knowledge and skills.

2. ICT contributes a great deal to working to automate and/or simplify the processes that people use as they solve the problems that they encounter in their everyday lives, jobs, and soon. Thus, people living in an Industrial/Information Age society need a significant level of ICT knowledge and skills relevant to such problem solving in their everyday lives.

It is the second situation that underlies the purpose of this 25-year old book and my current comments given here. A modern education needs to include a major focus on problem solving situations that a person encounters in their everyday lives. When new tools—in this case, ICT tools—are developed, they are both a source of new problems and an aid to representing and solving old and new problems.

Some of the new tools are so transparent (easy to use, easy to learn how to use) that no school time need be spent in learning to use the tools. For example, I doubt if you needed to take a course in order to learn to use a cell telephone. But, others of these tools take some, and

perhaps a great deal of time and effort to learn to effectively use. It is here that formal education can make a difference. And, it is here where our schools are doing poorly.

I’ll close with one simple example. In their everyday lives, quite a few people encounter “simple” computation tasks such as adding fractions or calculating the sum of products of pairs of numbers. Some of the former types of calculations are trivial, such as 1/6 + 1/3 = 1/2. Some can be done mentally. Some can be estimated accurately enough to effectively deal with the situation.

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paper. As an example, probably you cannot readily do the following calculation in your head: (23.5 x 14.8) + (16.9 x 54.3) + (83.6 x 31.4)

Indeed, you might find it to be a reasonably challenging paper and pencil activity, and perhaps you would produce a result that is not correct.

However, this is an easy activity that can be accomplished quickly using a calculator and without use of paper and pencil. That is because almost all inexpensive 4-function calculators have a M+ key and a MR key. Here, M stands for “memory.” The calculator has a memory location where it can store an answer, roughly in the same way that you would write down an answer, and then use it later. To do this calculation, key in 23.5 x 14.8 = and then the M+ key. The result of the multiplication is added to the memory location (which began at zero, if you just turned on your calculator and/or cleared the memory). Continue by keying in 16.9 x 54.3 = and then M+. The second multiplication is done and the result is added to the current number in the memory. Continue by keying in 83.6 x 31.4 = and then M+. Finally, key MR (memory recall) and the final answer is displayed.

The same general approach works for adding fractions.

As you can see, it is easy to learn to use the M+ and MR keys to work with the memory location in a calculator. It takes a few minutes of instruction to learn to do this. Most adults who own calculators have not learned to use this feature of their calculators! In my opinion, this represents a (small, easily correctable) flaw in our formal educational system. Also, it means that students are not getting a chance to learn a little bit about computer memory (which is the same as calculator memory). They are getting a school-taught or self-taught knowledge of calculators as “black box” that sort of magically can do routine calculations and calculate square roots. I am saddened by the fact that our school system has not done better over the past 25 years.

This same “black box” approach is being used in much of the computers in education instruction that students are receiving. I strongly believe that we can do better.

David Moursund January 2005

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Preface to the 1980 Edition

Most elementary school teachers are people-oriented, and are not particularly machine-oriented. They are vitally concerned with children, in helping children to develop their potentials and to learn. It is not surprising, then, that many elementary school teachers view computers and calculators with suspicion. Will computers help students to learn more, better, faster? Will use of calculators lead to a better understanding of mathematics and increased problem solving skills? Will calculators and computers dehumanize education? The answers to these questions are both yes and no. Much depends upon the teacher, the student, the equipment, the instructional

materials, and so on. The knowledge, attitude, and skills of the teacher are apt to be the dominant factors.

Ten years ago questions about instructional use of calculators and computers were of academic interest, but did not concern the ordinary elementary school teacher. Calculators and computers were too expensive, and were not even readily available in high schools. Their impact upon most elementary schools was zero. But the price of both calculators and computers has declined rapidly, so that now good quality calculators cost under $10, and computers are

beginning to become a common household item. Calculator and computer usage is commonplace in many junior high schools and high schools. It is no longer appropriate for elementary school teachers and elementary schools to ignore their potential uses in instruction.

Perhaps the most difficult questions have to do with what children should learn to do

mentally, what they should learn to do using books, pencil and paper, and what they should learn to do using other aids such as calculators and computers. The capabilities of these electronic machines continue to grow rapidly and their price is now quite affordable. Thus the whole content of the elementary school curriculum needs to be rethought, and substantial revision may be necessary. This booklet is written for preservice and inservice elementary school teachers who have had no formal training in the computer field. It is designed to help such people gain an initial level of computer literacy and to lay a foundation for additional learning. (Teachers with some computer experience may find the booklet provides a useful overview and some food for thought.) After an introductory section, the main part of this booklet consists of a sequence of questions; each question is followed by a brief answer and by a longer, more detailed answer. The latter part of the booklet is a long section containing sample activities that can be used in an elementary school classroom or in a teacher-training situation. The booklet ends with a Brief Guide to Periodical Literature and a Glossary.

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Introduction

This booklet is written for preservice and inservice elementary school teachers. Thus we will assume that you fall into one of those categories and speak directly to your needs. We will assume that you have used a calculator; it is desirable that you also have had some hands-on experience with a computer. A half hour's interaction with a computer will add substantial meaning to what follows.

Many elementary schools have access to computers for instructional purposes. In the next few pages we describe a hypothetical interaction between a fourth grade student and a computer. The computer might be a self-contained microcomputer, costing $1,500 or less. Or the student may be interacting with a very large computer via telephone line to a terminal in the classroom.

As you walk into the fourth grade classroom you see a student just sitting down in front of a TV set with a typewriter keyboard. You look over the student's shoulder at the TV display screen.

MENU OF DRILL AND PRACTICE PROGRAMS 1. ARITHMETIC 2. GEOGRAPHY 3. HISTORY 4. READING 5. SPELLING 6. VOCABULARY

PLEASE TYPE A NUMBER BETWEEN 1 AND 6

The student is obviously familiar with the computer equipment. Almost before you finish reading the directions s/he types the number 1. The printing on the TV screen disappears, but then is immediately replaced by some more printing.

GOOD! I AM PLEASED THAT YOU WANT TO DO

SOME ARITHMETIC. PLEASE TYPE YOUR NAME AND THEN THE ENTER KEY

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You watch as the student rather laboriously types TERRY JOHNSON and pushes the ENTER key. After a couple of seconds the computer responds.

I HAVE CHECKED MY RECORDS, TERRY, AND THEY SHOW THAT YOU NEED TO WORK ON YOUR TIMES FACTS. IF THAT IS ALL RIGHT WITH YOU, TYPE THE LETTER Y FOR YES.

OTHERWISE, TYPE THE LETTER N FOR NO

Terry, being an obedient and rather docile student, types the letter Y.

VERY WELL, TERRY. I WILL GIVE YOU A ONE

MINUTE SPEED DRILL. WORK AS FAST AS YOU CAN, BUT TRY TO NOT MAKE ANY ERRORS. AFTER YOU TYPE AN ANSWER YOU MUST PUSH THE ‘ENTER’ KEY.

WHEN YOU ARE READY TO BEGIN, PUSH THE ‘ENTER’ KEY.

You see Terry take several deep breaths, poise one hand over the digit keys on the keyboard, and push the ENTER key. The TV screen clears and a multiplication problem is displayed. Numbers in the upper left corner of the screen begin to count off seconds, and display a scoreboard of Terry's results.

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3 SECONDS 2 RIGHT 0 WRONG 6 x 2 ?

You watch as Terry completes 37 problems in one minute. Each wrong answer results in a "bleep" from the computer, along with a display of the problem correctly solved. You also notice that the same problem appears again a few seconds later. At the end of one minute the computer displays the results.

VERY GOOD TERRY! YOUR SPEED AND ACCURACY ARE BOTH BETTER THAN

YESTERDAY. YOU DID 37 PROBLEMS WITH ONLY THREE ERRORS.

WOULD YOU LIKE TO TRY ANOTHER

MINUTE OF MULTIPLICATION DRILL? TYPE THE Y KEY FOR YES OR THE N KEY FOR NO.

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MENU OF DRILL AND PRACTICE PROGRAMS 1. ARITHMETIC 2. GEOGRAPHY 3. HISTORY 4. READING 5. SPELLING 6. VOCABULARY

PLEASE TYPE A NUMBER BETWEEN 1 AND 6

As you continue to observe Terry types a 2 and enters into a geography lesson. The computer draws a map of the western United States and then asks "WHAT IS THE NAME OF THE LARGEST STATE SHOWN ON THIS MAP?" When Terry responds CALEFORNYA the computer responds "YOUR ANSWER IS CORRECT BUT YOUR SPELLING IS TERRIBLE. I SUGGEST YOU SWITCH OVER TO A SPELLING LESSON."

Does this seem like science fiction to you? It isn't. It is a rather routine use of computers as an aid to learning. A few schools have had computer facilities such as this for many years. Now that microcomputers are cheaply available, the use of computers as an aid to instruction in the elementary school is growing rapidly. Computers are now an important part of the daily education of many children. Terry was interacting with the computer in a computer assisted learning (CAL) mode. CAL can help students to learn more, better, and faster. But computers are having other impacts upon the elementary school.

This booklet addresses questions such as "How should the content of the elementary school curriculum change to reflect the capabilities of calculators and computers?" and "What should students be learning about calculators and computers?" The use of computers in education is now a well-established field, and one could well spend a lifetime studying just this aspect of

education. Thus this booklet will not teach you all about computers, or all about computers in education. But it will get you started and it will provide a foundation for future learning.

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What is a Computer?

A computer is a machine designed to work with letters, digits, and punctuation

marks. Thus it can work with words, numbers, and anything else that can be

represented by these symbols. A computer can rapidly and accurately follow a

detailed set of directions that has been stored in its memory. It is a general purpose

aid to problem solving, with potential uses in every academic discipline.

Graphic by Percy Franklin

It is assumed that you are familiar with a handheld calculator that can add, subtract, multiply, and divide. This is an electronic calculating device, since it runs off of electricity and the

calculation circuitry has no moving parts. It is a digital calculating device since it works with individual digits and with numbers represented by a sequence of digits. A handheld calculator is a marvelous device. It is cheap, reliable, useful, and easy to learn how to use. But it is not a computer! Now imagine adding a typewriter keyboard to a calculator, so that it can work with letters and punctuation marks as well as with digits. Imagine automating it, so it can

automatically follow an intricate set of directions, and then increasing its speed many fold. Now you have a computer! A computer is a machine designed for the input, storage, manipulation, and output of symbols (digits, letters, punctuation). It can automatically and very rapidly follow a step-by-step set of directions (called a computer program) that has been stored in its memory.

The main emphasis in this booklet is upon computers, but we will also cover the topic of calculators in education. Calculator and computer equipment spans a wide price range, and varies widely in capability. One can buy a handheld calculator for $6 or less, while the most expensive computer systems cost a million times as much, or more. The cheapest calculator and the most expensive computer have quite a bit in common, since they both make use of electronic components for storing and manipulating symbols. But it should be evident that a cheap

calculator is no match for a computer in solving problems that can make full use of a computer's capabilities.

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We will study these capabilities and their educational implications. Some of the key ideas are as follows.

1. A computer can store a very large amount of data – useful in solving a wide variety of problems.

2. A computer can automatically follow a very long and very complicated set of directions specifying how to solve a certain type of problem. Large libraries of such computer programs are now readily available.

3. A computer is very fast. Even the least expensive computer can carry out many thousands of program steps per second.

4. A computer is a general purpose aid to problem solving. It is a useful tool in every academic discipline.

This last point is very important to keep in mind. We understand and accept that reading and writing are general-purpose skills, and that pencil and paper are a general purpose tool.

Eventually computers will gain a similar level of acceptance, and skill in their use will be expected of all educated people.

At one time calculators were quite expensive, and consequently their potential impact upon elementary school education was low. It was unthinkable that students be given significant access to calculators costing $1,500 apiece, when most adults could not have similar access. Now, of course, calculators are commonplace in homes, stores, and wherever calculation needs to be done.

The price of a microcomputer is now about what calculators cost in the mid 1960's. While computers will never be as cheap as handheld calculators, their price continues to decrease. They are increasingly available in homes, businesses, and in education at all levels. Over the next 20 years they will have a massive impact upon education.

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What is Interactive Computing?

Early models of computers could be used by only one person at a time, and

little or no interaction between the user and the machine could occur while the

machine was working on a problem. The development of timeshared computing

allowed many people to simultaneously share a computer's facilities, and to

interact with the machine as it worked on their problems. In the mid 1970's a new

type of computer, called a microcomputer, was developed. It is designed to be used

in an interactive mode, but by only one person at a time.

The first general purpose electronic digital computer became operational in December 1945. It contained 18,000 vacuum tubes, filled a very large room, used an enormous amount of

electricity, and required extensive air conditioning. To set up the machine to work on a particular type of problem might take a week or more. Thus a very limited number of people were able to use the machine to help solve their problems.

Computers first became commercially available in 1951, and transistorized computers became common starting in 1958. Thus machines became smaller, more reliable, and required less electricity and air conditioning. Still, only one person could use a machine at a time, and the setup time between jobs remained a problem. There was little or no opportunity for a person to interact with the machine while it was actually solving a problem. Two developments during the 1960's had a major impact upon the computer field. First came the idea of sharing a computer's resources among a number of simultaneous users. The machine is designed to handle a number of input and output units, and to interact with a number of simultaneous users. This is called timeshared computing, or INTERACTIVE computing. A timeshared computer network can also serve as a communication system, and that idea is now commonly used in modern business communication systems.

The second development was the integrated circuit. The same ideas used to manufacture a single transistor could manufacture a circuit containing dozens or even hundreds of transistors and other components. These are manufactured on a small piece of silicon, called a chip. Progress in chip technology led to the capability of building very complex circuits from a small handful of chips, plus appropriate connectors and power supply. Moreover, since these chips

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became cheaper and cheaper to manufacturer, the price of computers decreased rapidly. Going into the 1970's, then, we had two main types of computer systems. The timeshared system was designed to allow a number of simultaneous interactive users, and shared its central memory and computing facility among these users. Alternatively, there were one-user-at-a-time systems, called batch processing systems. The setup time between users was reduced to a few seconds or less in many cases.

The early 1970' s saw the introduction of smaller, less expensive computers, called minicomputers. Such machines began to be used in secondary schools, and became

commonplace in higher education. Chip technology continued to progress, and the mid 1970's saw the introduction of microcomputers—machines whose electronic circuitry was based upon a very small number of chips. These microcomputers are so inexpensive that they can be used in a combination batch processing-timeshared mode. Thus a single user has full control of the

machine over an extended time span, and interacts with it much in the manner of interacting with a timeshared system. The user has some of the advantages of both a batch processing and a timeshared system, but also certain disadvantages. The communication between simultaneous users of a timeshared system is lacking. The large storage capacity and versatility of larger computers (typically available on both batch and timeshared systems) is missing. Still,

microcomputers are revolutionizing the field of computers in precollege education. Their price is sufficiently low so that every school system can afford to provide some computer facilities to its students. The interactive nature of microcomputers has proven to be an excellent aid to

education.

All teachers understand that students need feedback to help them learn. This feedback can be provided by a teacher, other students, answer sheets, and so on. An interactive computer system is an excellent feedback mechanism. It can digest and process complex student responses, and then provide feedback appropriate to the situation. It is the interactive aspects of computers that provides the potential for a revolution in instruction.

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What is Computer Hardware?

A computer system consists of physical machinery (called hardware) and

programs (called software). Both are needed if a computer system is to perform a

useful task. The key hardware components are given in the diagram. They include

input unit(s), output unit(s), memory, and a central processing unit.

When one looks at computer one sees the hardware—the physical machinery. Every general purpose computer system has five major hardware components.

Input unit(s): To get information into the computer. The most common input unit is an electric typewriter device called a keyboard terminal.

Output unit(s): To get information out of a computer. The most common output devices are a television display screen (color, or black and white) and a typewriter-like printing mechanism.

Primary storage: Contains a program while it is being executed, and contains the data being processed.

Central processing unit: Figures out the meaning of the instructions in a program, and carries them out very rapidly.

Secondary storage: Provides permanent, inexpensive storage of large libraries of computer programs and large quantities of data.

The least expensive microcomputer systems, costing under $500, have all five of these components. For an inexpensive microcomputer system the input unit will be a typewriter-style keyboard, perhaps molded into a cabinet containing a television display screen. The output unit is a television display screen, perhaps specially modified to improve the quality of the display. Secondary storage is a cassette tape recorder, using inexpensive cassette tapes. The central processing unit is a single chip, called a microprocessor. Such chips may cost less than $10 apiece when mass produced. The primary storage is relatively limited in total storage capacity, and is manufactured using chips.

A key aspect of computer hardware is its speed. Even the least expensive microcomputer can execute many thousands of instructions per second. The most expensive computer systems are perhaps a thousand times as fast as microcomputers, being able to execute tens of millions of instructions in one second.

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One measure of the capability of computer hardware is the capacity of primary storage. This type of memory is relatively expensive, since it must function at the same high speed as the central processing unit. On an inexpensive microcomputer system one expects to find a primary storage capacity of between 8,000 and 64,000 characters (that is, letters, digits, or punctuation marks). A large computer system will have a primary storage capacity several hundred times as large.

The large scale computer system has a number of additional hardware features that help to improve its overall capability. For example, it will have a line printer that is many hundreds of times as fast as an electric typewriter. Printing speeds of many thousands of words per minute are possible. It will have very high quality, large capacity, magnetic tape units. It will make extensive use of disk storage units, which are flat circular plates coated with the same material used on magnetic tapes. The total secondary storage capacity of the system may be comparable to a large library - that is, the equivalent of hundreds of thousands of books.

There are many input/output devices that can contribute to making a computer system a good educational tool. Very young children can learn to use a keyboard terminal. But a touch panel, which recognizes which spot on a display screen has been touched, may be more appropriate to their needs. Similarly, a bit pad, which allows a drawing to be entered into a computer, is a useful educational tool. Many computer systems have an audio output device, perhaps one that can make a buzzing noise. But some computer systems can output a full range of musical tones as well as the human voice. Also, voice input to computer is now quite feasible. It should be recognized that the variety of input/output hardware mentioned above costs money, although not an unreasonable amount. Also, this hardware is useful only if appropriate computer programs (software) are available. Software is discussed in the next section.

A recent, very exciting addition to computer hardware is the videodisc. Designed initially for the storage and playback of television programs, the videodisc is also an excellent secondary storage device for computers. A laser readout, computer controlled videodisc system can store 50,000 pictures—the equivalent of a half hour of motion pictures. Under computer control one can get random access to single pictures and/or show the materials at various speeds, forward or backward. The videodisc system has two sound tracks, useful in bilingual instruction and for other purposes. Eventually videodiscs will help bring high quality computer assisted instruction into homes and schools throughout the country.

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What is Computer Software?

A computer program is a detailed step by step set of instructions specifying how

to solve a certain type of problem. The terms "computer program" and "computer

software" mean the same thing. A computer can solve a problem only if

appropriate software is available. In the United States alone, nearly a half million

people are involved in the occupation of writing computer software. These people

are good at figuring out how to solve problems and at writing detailed sets of

instructions. They must have good knowledge of the subject matter of the problem

area. A very important aspect of computers is that computer software can be stored

in a library, typically in a computer's secondary storage hardware. This software is

then available for people to use - people who did not write the programs. Thus one

can use a computer without knowing how to write programs. This is essential to

the elementary school, where neither the typical teacher nor the typical student has

the knowledge to develop the needed software.

Graph by Percy Franklin omitted to decrease Web retrieval time needed for this document.

Computer programs are written in computer languages such as BASIC, COBOL, machine language, or PASCAL. Programming languages are discussed in the next section of this booklet. At one time the primary cost of using a computer was the cost of the hardware, but now software is often the dominant cost. Of course, the same software may be used by thousands of people, in which case its cost may be spread out over a large number of people.

To better understand software, we need to understand two things: 1. What types of steps or operations can a computer's CPU carry out?

2. What is involved in writing software to solve a particular type of problem?

A computer is a machine designed to work with symbols, such as letters and digits. A computer's CPU can move these symbols between various primary and secondary storage units; it can accept these symbols as input and produce strings of symbols as output. It can combine letters to form words or digits to form numbers. It can add, subtract, multiply, and divide numbers. It can decide if two symbols are the same, or if a letter comes earlier in the alphabet than another letter. A CPU is not "intelligent" like a human being. It merely mechanically and rapidly carries out certain simple manipulations of symbols.

If a computer is to solve a problem or help solve a problem then its CPU must be told

precisely what it is to do. Thus a human being must figure out how to solve the problem and also figure out what to tell the computer to do. A computer programmer is a person who knows how to solve problems, and who is good at writing detailed sets of instructions in a form that a computer can follow. Thus a programmer must have good insight into the capabilities and

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limitations of a computer's hardware and its programming languages. Equally important, a computer programmer must understand the subject matter field containing the problem. For example, if s/he is to write a program to solve a business problem, the programmer is apt to need to know a lot about business.

A very key concept, however, is that people other than computer programmers can use computers. Once a program has been written to solve a particular type of problem, it can be stored in a computer library. This means that it is placed into a computer's secondary storage system, and can easily be brought into primary storage for use as needed. One does not need to know how to write programs in order to make use of a program from a computer library. Very young children can easily learn this aspect of using a computer. It is not much more difficult than using a TV set or a record player.

The educational implications of this are immense. A major goal of education is to help students learn to solve a wide variety of problems. Now we have machines that can solve many of these problems. The capabilities of these machines continue to grow as more and better programs are written, and as better hardware is developed. If a computer can solve a certain type of problem, what do we want people to know about solving the same problem using pencil and paper, or mentally?

One quite important branch of computer science is called artificial intelligence. It deals with how smart a computer can be—can it do intelligent-like things? Computers can play complex games such as checkers and chess quite well. They can perform medical diagnoses, carry on a conversation, and aid in foreign language translation. Progress in artificial intelligence research is continually expanding the horizons of computer capabilities. Needless to say, artificial intelligence has the potential to have a significant impact upon education.

One of the most complex problems faced by our society is helping students to learn. Writing computer programs that will help students learn is not an easy task. Fortunately, there are now many professional educator-programmers who are working on the problem. The supply of commercially available, high quality educational software is gradually expanding. Currently, however, there is a shortage of software designed to fit the wide variety of instructional needs that exist in elementary school education.

Remember that a computer program is a detailed set of directions, telling what to do at all stages of solving a certain type of problem. Suppose that the "problem" is to help a student learn reading or arithmetic. Do we know enough to mechanize the process? It is easy to see from this question why it is difficult to develop good quality software for use in elementary education. One needs to know the subject matter, learning theory, children, and the computer. Because of the broad range of knowledge and talents necessary, software is often developed by teams. A team might consist of a teacher, a media specialist, a learning theorist, and a computer programmer. Such a team, properly experienced in working together, can produce very high quality

educational software. But because of the large amount of labor involved in its development, good quality educational software tends to be quite expensive.

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What are Programming Languages?

The CPU of a computer "understands" (that is, can interpret and carry out)

perhaps 60 to 300 different instructions. This is the machine's "machine language,"

and different brands or models of computers generally have different machine

languages. A number of "universal" languages, with names like BASIC, COBOL,

LOGO, PASCAL, and PILOT have been developed. Programs written in these

languages can be used on a wide variety of makes and models of computers. This

is made possible by certain translating programs, which translate from these

languages into machine language. A different translating program is needed for

each programming language, and also for almost every different make or model of

computer.

Without appropriate software a computer can do nothing. Thus a major aspect of the history of computers is the development of better aids for programmers. Programming in machine language is slow and error prone. Programs written in the machine language of one machine will not run on a machine with a different machine language. Out of this difficulty arose the idea of "higher level" languages - programming languages that would be independent of any particular machine.

Beginning in the 1950's computer scientists have developed a large variety of these higher level languages. FORTRAN was developed for scientists, COBOL for business people, BASIC for college students, LOGO for elementary school students, and PILOT for educators. New languages have been developed as computer scientists gain better insight into the capabilities and limitations of computers and the particular people who will use the languages. A language designed to fit the needs of a first grade student is not apt to fit the needs of a research scientist. A language designed to aid in music composition is not apt to fit the needs of an architect.

The language BASIC was developed at Dartmouth College in the early 1960's to meet the interactive computing needs of college students. Since then the use of BASIC has grown rapidly, so that it is the most widely used language in education at all levels. This in no sense implies that it is the best language for use in precollege education - merely that currently it is the most used language. If a language such as BASIC is to be used on a particular computer then there must be a translating program, which translates BASIC statements into that machine's machine language. The sample BASIC program given below can be run on dozens of different types of computers because dozens of different translating programs have been written for BASIC.

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Page 19 100 REM *** PROGRAM RECTANGLE ***

110 REM * DESIGNED TO ILLUSTRATE PROGRAMMING IN BASIC 120 REM * PROGRAM WRITTEN BY DAVID MOURSUND

130 REM * VARIABLES

140 REM * A = AREA OF A RECTANGLE 150 REM * L = LENGTH OF A RECTANGLE 160 REM * W = WIDTH OF A RECTANGLE 170 REM * P = PERIMETER OF A RECTANGLE

180 PRINT “THIS PROGRAM WORKS WITH RECTANGLES.” 190 PRINT “YOU SUPPLY THE LENGTH AND WIDTH, AND”

200 PRINT “THE COMPUTER DETERMINES AREA AND PERIMETER.” 210 PRINT “WHAT IS THE LENGTH OF THE RECTANGLE?”

220 INPUT L

230 PRINT “WHAT IS THE WIDTH OF THE RECTANGLE?” 240 INPUT W

250 REM * USE FORMULAS TO COMPUTE THE AREA AND PERIMETER. 260 LET A = L *W

270 LET P = 2*L + 2*W

280 PRINT "THE AREA OF THE RECTANGLE IS"; A 290 PRINT "THE PERIMETER OF THE RECTANGLE IS”; P 300 PRINT

310 PRINT “WOULD YOU LIKE TO SOLVE ANOTHER RECTANGLE (YES, NO)” 320 INPUT R$

330 IF R$=”YES” THEN 210 340 IF R$=”NO” THEN 370

350 PRINT “YOUR RESPONSE IS NOT UNDERSTANDABLE.” 360 GO TO 300

370 END

When this program is run on an interactive computing system it will print out directions to the user, request values for the length and width of a rectangle, and then compute and output its area and perimeter. The user of the program does not need to remember the details of how to solve the problem. The program can be used to solve a sequence of rectangle problems, and it halts when the user indicates there are no more rectangles to solve.

A single computer can "understand" any number of different languages. All that is necessary is that the appropriate translating programs be written. But writing a translating program may take several years of a full time, very skilled, programmer's effort. Thus translating programs are quite costly. The manufacturer of an inexpensive computer system is apt to provide translators for one or two languages. The owner of the machine may need to purchase additional translators, or pay to have them developed, if s/he wants to have other languages available for use on the machine.

Students at all grade levels can learn to program, provided that appropriate computer facilities, teaching and learning aids, and trained teachers are available. Some instruction in

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amount of instruction in computer programming to develop a functional level of skill, such as would be useful in writing programs to solve problems in a variety of disciplines. Thus computer programming as a part of computer literacy might be part of a quarter or half year computer literacy course in a junior high school, while computer programming to develop a useful skill level might be incorporated into a year long senior high school computer science course.

At the current time there are very few elementary school teachers who are qualified to teach computer programming. There are few instructional materials suited to the needs of elementary school students or teachers. Moreover, there is little agreement as to whether students at this level should be taught to write programs. It seems likely that eventually there will be

programming languages that are well suited to the needs of young students. If teachers become skilled in the use of and instruction in these languages, then perhaps computer programming will eventually become a standard part of the elementary school curriculum.

We mentioned earlier that LOGO is a language that was designed for use by young students. It was developed by Seymour Papert at Massachusetts Institute of Technology. Using this language students can draw pictures on a TV screen, solve problems involving words and numbers, and so on. If appropriate output devices are available they can cause a mechanical turtle to move around on the floor, ring a bell, or program an electronic organ to play music. The computer equipment creates an interesting and "rich" problem solving environment. Papert feels that students who are immersed in this environment will develop their problem solving skills and will be strongly motivated to learn to program a computer. His research findings support this position.

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What Are the Main Categories of Educational Use of

Computers?

The educational use of computers can be divided into administrative,

instructional, and research uses. Higher education in the United States spends

about 3% to 4% of its entire budget on computing, with funds fairly evenly

distributed among these categories. The typical precollege school system spends 1

% to 2% of its budget for computing. Generally administrative use currently far

exceeds instructional use, and there is relatively little research use of computers in

school systems. Very few school districts in the United States currently spend as

much as 1 % of their budgets for instructional use of computers. However, this

type of usage is now growing quite rapidly.

It is assumed that you are most interested in instructional uses of computers, so the next three sections of this booklet are devoted to various instructional aspects of computers. In the current section we discuss administrative and research uses of computers in education.

Almost all school districts in the United States make administrative use of computers. Detailed records must be kept, and reports must be filed with the state government. Teachers must be paid, and tax records must be filed with the federal government. Student records must be maintained, and grade reports must be sent to parents. Inventories of supplies, books,

instructional materials, etc. must be maintained and accounted for. All of these tasks can be accomplished using "by hand" methods. But often use of a computer accomplishes the task cheaper, more accurately, and more rapidly.

School administrators need rapid access to accurate information to aid in decision making. The idea of a computerized management information system is now common in business and industry, and is gradually coming into school systems. Data that may be needed for decision making is collected and stored in a computerized information retrieval system. Software is developed to allow the processing of this data. With a good computerized management

information system an administrator can easily get answers to "what if" questions, such as "What if Bus #7 doesn't run today due to snow?" or "What if substitute teacher's salaries are raised 15%?" Because computers are such useful aids to school administrators we can expect their use to increase rapidly in the years to come.

Computers are an essential tool to research in higher education, with about one-third of higher education computing budgets being used for this purpose. Relatively little research goes on in precollege educational systems, and hence little money is spent for computer usage in this category. But this type of usage is growing. We will cite two examples.

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centers, called ERIC centers, which subscribe to almost every educational journal and which seek out literature on educational research. These centers hire people to write summaries of the research articles and to index the articles. All of this information is put into a computerized information retrieval system, and hence made easily available to researchers.

For example, suppose you were interested in bilingual, bicultural education in the elementary school. A computerized search of this topic in the ERIC data bank might cost $15. In a few minutes you could receive titles and brief abstracts of a number of current articles in this area. The same computer system can even be used to place an order for microfilm copies of the articles! There are now hundreds of computerized data banks of bibliographic information. Moreover, major libraries, such as the Library of Congress, have switched to a computerized replacement of the card catalog systems.

A second typical research use of computers is in the statistical analysis of educational data. A school system decides to institute a special program of instruction in some of its schools. Tests are administered to students entering the special program as well as to a control group of similar students who will not be in the special program. Later all of these students are tested again, and compared to see what types of changes have occurred. Computers are an essential tool to working with large sets of data and performing the necessary statistical analysis.

Both administrative and research use of computers in education illustrate an important point. Computers are a tool that may be useful in attacking certain problems. Usually these problems are already being handled by some other (non computerized) means. Thus one has a choice—to use or not to use a computer. The decision to use a computer should be based upon a careful study that considers the advantages and disadvantages of computer usage. Merely because a computer can be used to help accomplish a specific task does not mean that it should be. Keep this idea in mind as you study various instructional aspects of computers.

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What Impact Should Computers Be Having On the Current

Curriculum?

The first and foremost goal of education is to give students the tools, skills, and

knowledge to cope with the types 01 problems faced by people in our society. Both

professional educators and the general public agree that reading, writing and

arithmetic are essential to understanding, representing, and solving problems.

From early on humans have devised and used tools to help solve problems.

Now calculators and computers have developed—mainly to help solve adult types

of problems. Elementary school education must decide role these what machines

will play: what students will learn to do mentally, what they will learn to do using

simple tools such as paper, and what they will learn to do using tools such as

books, calculators, and computers.

Calculators and computers are an everyday tool of adults working in business, government, and industry. Our educational system has yet to understand the educational implications of this fact. Changes need to be made in our curriculum even if we are not yet able to make calculators computers readily available to all students.

While education has many goals, it is generally a important one is to give students the tools, skills, and with the types of problems faced by people in our society. Thus we have a major emphasis upon the three R's, and upon learning to learn.

It is problem solving, and learning to cope with a wide variety of problems, that is at the heart of education. The major steps involved in problem solving include:

1. Understand the problem. Here reading and listening are essential skills, and overall general education plus common sense are important.

2. Figure out a plan to solve the problem, and represent the plan. Here thinking, drawing upon previous knowledge, and writing are essential skills. One (new) way to represent a plan is in the form of a computer program.

3. Carry out the plan. Often this is a routine and rote task. Speed and accuracy are desirable, while perseverance and attention to detail are often necessary.

4. Understand the meaning of the results, check to see if they make sense, and make use of the results. This is a thinking task, drawing upon previous knowledge and one's

understanding of the problem to be solved.

Of these four steps, the easiest to teach and the easiest to test on standardized tests is step 3. Also, it is evident that this step is essential if a problem is to be solved. Thus it is not surprising

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is precisely what calculators and computers do best!

We can gain insight into the overall curriculum impact issue by considering calculators in the elementary and middle school. It takes a number of years of instruction and practice for students to master paper and pencil algorithms for multiplication or division of numbers containing decimal fractions, or for calculating a square root. There is a clear difference between

understanding the concepts of these operations (what problem is being solved, why does one want to solve it) versus mastering a paper and pencil algorithm. Calculators provide an alternative. Perhaps it is not a necessary or appropriate use of school time to have students master those paper and pencil algorithms. Perhaps the time might better be spent in improved mental arithmetic skills, better understanding of what problem is being solved, and more experience in problem solving.

The electronic digital watch and clock provide another interesting example. Young children can learn to "tell time" (state the numbers representing the time) very easily from a digital readout. But clearly this is different from "understanding" time or solving problems related to time. Thus a digital watch does not solve the problem of teaching students about time any more than a calculator solves the problem of teaching students arithmetic. But both the digital watch and the calculator are valuable tools, and each requires that some rethinking/restructuring be done in the curriculum.

The ready availability of computers broadens the scope of areas in which curriculum revision may be necessary. Word processing (a computerized typewriter) provides an interesting

example. A modern word processing system consists of a keyboard terminal, a TV display screen, a typewriter-quality printer, and a secondary storage device such as a magnetic disk. Material is typed into the computer and displayed on the TV screen. Corrections are easily made. The computer can even be asked to check for possible misspelled words! Then the material is printed out on paper using the typewriter printer.

A word processing system greatly increases the productivity of a writer or secretary. Its potential impact upon students learning to write is quite large. Should typing be taught in the elementary school? If a computer can check one's spelling, does spelling remain at its current level of importance? How important is good penmanship if typewriters or word processing systems are readily available?

Still another interesting example is provided by a computer system attached to a music synthesizer. It may well be that many young children have the capability of composing music. But most don't develop this talent, since they lack the skills to perform or represent the music they can create in their minds. An interactive computer system can solve both of these problems. The use of such equipment in the elementary school curriculum might significantly change music education.

We have machines throughout our society, such as the car, train, airplane, typewriter,

telephone, radio, television, telescope, and microscope. Our educational system teaches students to work with these machines, rather than to compete with them. So it will eventually be with calculators and computers. Our overall curriculum needs to change, to reflect the role that calculators and computers best play in problem solving. This means that we must decrease the emphasis upon the routine and rote skills of carrying out a plan to solve a problem. We need to place increased emphasis upon the higher-level skills of understanding, figuring out how to solve

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problems, representing plans to solve problems, and understanding the meaning of results produced when these plans are carried out.

Two points need to be made clear. First, paper and pencil remain an essential tool—it is merely routine and rote paper and pencil manipulation that is decreasing in importance. Second, there is increased need for accurate and rapid mental skills, such as knowing the basic number facts and knowing how to spell and punctuate. What we need to do is prepare our students to work with the computer tool, rather than to compete with it.

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How Are Computers Used as an Aid to Instruction?

The use of computers as an aid to instruction has been extensively researched

over the past 20 years. There is substantial evidence that computers are an effective

instructional delivery system. That is, with a broad range of conditions, students,

and subject matter, students learn better and faster with computers as compared

with "traditional" instructional delivery systems. This is highly dependent, of

course, upon having adequate and appropriate computer software and hardware.

Since software and hardware can be quite expensive, the cost effectiveness of

computer assisted learning is often questionable. But the low cost of

microcomputers make computers a feasible aid to instruction.

The overall field of teaching and learning using computers is called computer-assisted learning (CAL). Development and research in CAL began in the late 1950's. There have been several large federally funded projects and literally thousands of smaller CAL projects that have been carefully studied and reported on in the literature. For example, the PLATO project began at the University of Illinois in 1959 and is now commercially distributed by Control Data Corporation. Pat Suppes of Stanford University began to develop drill and practice materials for the elementary school in the 1960's. United States, distributed by the started by Suppes. Not every CAL project is successful. But in the overwhelming majority of cases students learn better and faster.

Until the advent of microcomputers, CAL was too expensive for widespread implementation in ordinary public schools and the home. Thus the great majority of CAL has been in medical schools, armed services education, remedial education, and so on where the cost of traditional education is high. Microcomputers have allowed two major changes. First, they have reduced the cost of hardware needed for CAL. by a significant factor. Second, they have broadened the potential audience (hundreds of thousands of microcomputers have been sold). This allows the cost of software development to be spread over a larger number of users and makes the

commercial development of CAL materials economically feasible.

Computer assisted learning is often broken into three parts, only two of which are apt to occur in an elementary school setting. Computer augmented learning is the easiest, quickest, and probably the cheapest instructional use of computers to implement. The idea is that students write programs and/or make use of computer library programs to help solve the types of

problems that arise in various academic studies. Since large libraries of such programs have been developed by use of people on the "real-world" (that is, people who have need to solve the problems on the job) such software is readily available. Students can learn to use it with a minimum of training, and the amount of teacher training that is needed is minimal. Computer augmented learning is quite common at the college level, and is beginning to creep into high

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schools. But elementary school students tend not to have much knowledge of real-world

problems that would require a computer for solution, nor do they have programming skills. Thus computer augmented learning is not of particular concern to elementary school teachers.

Computer managed instruction is any application of computers to classroom management or teacher support functions. A computer can score a multiple choice test, perform an item analysis on the results, and even print out individualized diagnostics for students. A computer can store grade records and print out summary statistics. A computer can keep track of each student's standing and progress in an individualized program of study. A computer can generate tests, and administer them to students in an individualized interactive fashion.

Computer managed instruction can aid teachers in much that is burdensome, time consuming, and relatively unrewarding in teaching. But it requires extensive software, keyed to the particular subject matter and instructional materials being used in the classroom. By and large this software is not currently available for elementary school education. Only slowly will it be developed, and initially it will be keyed to traditional nationally sold textbook series. Several major publishing companies are developing such computerized supplements to their textbooks.

Computer assisted instruction (CAI) is the use of computers to present instruction to students. It is the interaction between a computer system and students to help students learn new material or improve their knowledge of materials previously studied. At its simplest level much CAI is merely rote drill and practice, with the computer serving as a drill master and record keeper. There are many cheap alternatives to this, such as flashcards, students drilling each other, and handheld calculator-like arithmetic drill machines. Still, CAI drill and practice is a very effective aid to learning. At a more sophisticated level CAI can be thought of as a programmed text. Various materials are presented to the student based upon the correctness of answers to questions previously presented by the machine. A student's rate of progress is governed by his/her rate of learning the material. At the most sophisticated level there exist dialogue systems, in which the computer and student interact in higher level problem solving activities. Often these are

computerized simulations of real-world problems, such as controlling water pollution, running a nuclear reactor, fighting an insect infestation, running a business, and so on. Many of these simulations are quite realistic; interacting with them is exciting, and results in substantial learning.

CAI is a direct challenge to teachers and to much of traditional education. As more and more good CAI materials are developed and proven effective in widespread use, the current role of teachers in education will come under attack. Students will be able to have inexpensive, patient, interactive, personalized tutors to use at home, in public libraries, and in school settings. AI Bork, one of the leading proponents of CAI in the United States, predicts that by the year 2000 more than half of all instruction in this country will be via computer.

One can think of computer assisted learning as a further step in the automation of education. (Certainly books and the printing press represent earlier steps.) Undoubtedly it will disrupt the current, traditional system, and eventually it could displace some teachers. It seems likely that this will occur rather slowly - indeed, almost all changes in education occur rather slowly. Also, it should be recognized that teachers play many roles in education. While CAL can help fill some of these roles, it makes little or no contribution to others. The loving, caring, feeling teacher will be needed more than ever. The net effect can be that schools get better. Much will depend upon

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What Should Elementary School Students Learn About

Computers?

Leaders in the computers in education field agree that all precollege students

should become computer literate. This means they should learn about the

capabilities and limitations of computers; they should learn the social, vocational,

and educational implications and effects of computers.

Two levels of knowledge are important in precollege education. First is an

awareness level. Second is a working-tool, or functional level. An awareness level

can begin to be developed in elementary school, and can be integrated into each

subject matter the student studies. A functional level requires specific instruction in

use of a computer. It includes substantial hands-on experience, both in using

existing library programs and in writing programs to solve problems. There is a

still higher level of computer knowledge—the professional level. Training to be a

computer professional is currently carried on mostly at the post-high school level,

although a few high schools offer some professional level of training.

The question of what students should learn about computers has been studied by many professional groups over a period of years. There is nearly universal agreement that all students should become computer literate. But computer literacy is a nebulous concept; there is not universal agreement as to its meaning.

Historically, computer literacy tended to refer to an awareness level of computer knowledge. Students would read about computers, and learn about their capabilities, limitations, and

applications. They would gain insight into how computers are affecting the world, and the vocational/ educational implications of this upon individual students. This point of view was strongest when computers were still quite expensive, and it was not feasible to make hands-on experience available to most students.

Gradually educators have come to realize that computers are even more important than first suspected, and that students at all educational levels can learn to use a computer as an aid to problem solving. This has been coupled with the development of microcomputers and a continued rapid decrease in the price of computer hardware. As computers more and more become an everyday tool of millions of people it has become clear that we must raise our sights.

Nowadays the goal of universal computer literacy is a goal of a working knowledge—a functional level of knowledge about using computers. Progress towards this goal can begin in the elementary school.

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school has three microcomputers housed in the library or learning center, and a library of software appropriate to the needs of its students. A person working in the library or learning center knows the rudiments of using the microcomputers, and who to contact if maintenance or repair is necessary.

If the three microcomputers are fully used during school hours then a total of about 2700 hours of contact time, or nine hours per student per year, is available. How can this computer time be used to help raise the computer literacy level of students? Clearly an average student access of one hour per month is not going to have a significant impact upon a student's overall instructional program. That is not enough computer access for a significant CAI program. But the following goals could be accomplished.

1. Beginning at the first grade level every student will learn to check out a program disk or tape from the program library, turn on the computer system, load a program, run a program, and return the tape or disk to the program librarian.

2. Each month every student will have 15-20 minutes of use of drill and practice materials on a computer. The materials should be in a variety of subject matter areas and suited to the level of the student. Thus students will experience computerized drill in arithmetic, geography, history, spelling, vocabulary, and so on.

3. Each month every student will have 15-20 minutes of use of an interactive

simulation/game designed to help students learn some subject matter. These will be chosen to reflect a variety of subject matter areas and types of simulations.

4. Each month every student will have 15-20 minutes of use of a microcomputer for

recreational purposes. The student should have the choice of a variety of games suited to his/her hand-eye coordination, mental skills, and interests.

The overall result of this program of computer usage is that each student will learn to use a computer in a wide variety of application areas, and (probably) enjoy the overall process. A later section of this booklet contains a number of sample activities that can be carried on in a

classroom. These can be backed up by appropriate movies or other media aids. They will contribute significantly to student awareness of computers.

The schedule of microcomputer usage listed above is based upon a five hour day, 180 days per year. If students can have access to the machines before and after school, during the lunch period, and evenings or weekends, substantially more hands-on experience is possible. If a teacher in the school has a significant level of computer knowledge then a computer class might be offered to some students, or a computer club might be started.

The plan just discussed should not be taken as an ideal model. It represents one possible starting point, assuming a certain level of computer accessibility and a low level of teacher knowledge. If the school had only one microcomputer, the plan could be followed for 5th and 6th graders. With two microcomputers the plan could be used with students in grades 3-6. If more computer facility is available then CAI becomes feasible.

Over a period of time one can expect that both computer accessibility and teacher knowledge will grow. If a school system decides that CAI should be used, a considerably higher level of computer access will be necessary. In a typical CAI setting, some specified group of students have everyday access to a computer. For example, it is common to have students drill on

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arithmetic or on language art skills for 10-15 minutes each day. When the computer is not being used for CAI purposes it can be used to allow increased computer access by all students in the school.

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What Role Should Calculators Play in Elementary School

Education?

Although the dividing line between calculators and computers is not very

distinct, calculators are primarily an aid to performing mathematical calculations.

Thus, there greatest impact is upon the math curriculum. The National Council of

Teachers of Mathematics strongly supports their use throughout the school

curriculum.

At the elementary school level students can become familiar with calculators

and begin to develop skill in their use. Limited and judicious use of calculators

here can free up some time that can be spent on the "thinking" and other higher

cognitive levels of activities needed in mathematical problem solving. This

calculator usage can change the overall flavor or direction of the mathematics

curriculum.

Because the calculator has many computer-like features, it is a useful aid in

introducing certain computer topics. For example, the memory in a calculator with

4-key memory is quite similar to a computer's memory, and the calculator number

system is similar to the computer number system.

Calculators and other electronic aids to mathematical calculation are now an everyday tool of most adults who need to do calculations. Perhaps 30 million calculators a year are being sold in the United States. Some are so small that they are as easily carried as a credit card. An electronic digital watch with a built in calculator now retails for under $50. Some major educational issues are:

1. What should students learn about calculators? 2. When should they learn it?

3. When should students be allowed to use calculators?

The often-voiced fear is that widespread student use of calculators will lead to a dependence upon these machines, and a decrease in paper and pencil or mental arithmetic skills. The use of calculators has been studied in hundreds of research projects, and the results tend to allay the fears. Use of a calculator does not cause a student's brain to atrophy. Judicious use of calculators does not damage the curriculum - indeed, can contribute substantially to it.

At the primary school level (grades 1-3) calculators have only modest value. They are an additional math manipulative, an exploratory tool. Their occasional use can provide additional variety in the curriculum, and can serve as an aid to learning topics currently taught at this level.

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Primary grade students enjoy playing with calculators, and many consider them to be delightful toys.

During the primary grades students develop a concrete and intuitive understanding of the four basic arithmetic operations. If this understanding and awareness is focused upon real-world problems then students will encounter some computational tasks that they can understand but cannot solve. This is a good situation, and calculator usage here is desirable.

At the intermediate level (grades 4-6) it is useful to have classroom sets of calculators. Students can receive instruction in their use and begin to develop the skills necessary to have a calculator be a useful too/. Some decreased emphasis upon paper and pencil calculation can occur. This can be replaced by increased emphasis upon mental arithmetic (both exact and approximate) and upon problem solving. There can be increased emphasis upon areas of mathematics such as geometry, logic, and statistics.

By the time students finish grade school they can have good skills in using a calculator to perform the four basic functions. Also, they can learn to use the memory features of a 4-key memory system, and hence to deal with fractions and more complex calculations. This will require some classroom instructional time and a lot of practice. It requires a higher level of calculator knowledge than most elementary teachers currently possess. The issue of how much students should use calculators is still not settled. Many math educators suggest that virtually unlimited calculator usage in the intermediate grades and higher is both acceptable and desirable. This would cause a significant change in the curriculum, and they feel this would be a change for the better.

Other math educators are more cautious or conservative. They are quick to point out that the secondary schools and national testing services

Teacher s Guide to Computers in the Elementary School